Output vs Format vs Codec: what is the right combination?
1 - Explanation of why with MP3 output the WAV sound is missing but the AAC sound is audible
this could be a problem with that particular file, try converting it to mp3 using an external program like ffmpeg or audacity or even an online tool.
or try a matroska container with x264 video codec and mp3 audio codec.

2 - Understanding the differences between selections in Output section: MPEG vs H.264 since these seem to be the most common. Other formats are welcome :) (Frame server, XVid, AVI Raw|JPEG).

3 - Explanation of Encoding &gt; Format and Encoding &gt; Codec options, in relation to point 2. For example, why are you able to choose MPEG output and non-MPEG format and non-MPEG-non-&lt;format&gt; codec? This is VERY confusing.

a container like (mp4,mkv) contains n video streams and n audio streams encoded in a given format with a given codec,a codec is a coder and decoder.
think of a container like a .zip or .rar file
some containers don't allow certain combination of those codecs (like .webm can't have a video stream encoded in h.264 but allows a vp9).

blender offers you presets to make your life easier.
a mpeg-4 (.mp4) with h.264 and mp3 like in your screenshot is a valid combination and the reason h264 is common is because it produces better video quality with small sizes and is well supported by browsers and Operating systems.